1. Field of the Invention
This invention relates generally to blood flow measurement, and more particularly to a method and system for measuring instantaneous and average blood flow rates from digital angiograms.
2. Background of the Invention
Vascular disease is a major cause of death in the U.S. Each year, approximately 500,000 Americans die of sudden cardiac death alone, and the pathologic findings almost invariably implicate coronary atherosclerosis. Vascular disease is also associated with stroke, brain ischemia, hypertension, and loss of limb because of poor perfusion. However, many of these effects may be reversible or preventable if vascular disease is diagnosed early. Thus, detection of vascular abnormalities, such as stenosis (i.e., regions in which the vessel diameter is narrower due to plaque in the vessel), and evaluation of their severity could improve patient prognosis.
In angiography, a sequence of two-dimensional images of the vascular system (angiograms) are acquired by the projection of X-rays through blood vessels into which a bolus of a contrast material is being injected. The appearance of the blood vessels may be further enhanced by the subtraction of a pre-injection image from a post-injection image, so that the background anatomic structures are eliminated. In clinical practice, the severity of vascular disease is usually assessed by visual interpretation of angiograms. This subjective assessment of severity is, by its nature, inaccurate. Indeed, several studies have documented that there is a large intra- and inter-observer variability in the subjective visual examination of stenosis. To reduce the uncertainty of subjective evaluation of vessel diameters, computerized methods have been developed for quantitative analysis of angiograms. (See B. G. Brown, et al.: "Quantitative Coronary Arteriography: Estimation of Dimensions, Hemodynamic Resistance, and Atheroma Mass of Coronary Arteriograms", Circulation 55:231 (1974); J. H. C. Reiber, et al.: "Coronary Artery Dimensions From Cineangiograms: Methodology and Validation of a Computer-assisted Analysis Procedure", IEEE Trans Med Imaging MI-3:131 (1984); M. A. Simons, et al.: "Vessel Diameter Measurement Using Digital Subtraction Radiography", Invest Radiol 20:510 (1985); M. T. LeFree et al.: "Digital Radiographic Assessment of Coronary Arterial Geometric Diameter and Videodensitometric Cross-sectional Area", SPIE 626:335 (1986); E. L. Nickoloff, et al.: "Evaluation of a Cinevideodensitometric Method for Measuring Vessel Dimensions From Digitized Angiograms", Invest Radiol 22:875 (1987); H. Fujita, et al.: "Image Feature Analysis and Computer-aided Diagnosis in Digital Radiography. 2. Computerized Determination of Vessel Sizes in Digital Subtraction Angiography", Med Phys 14:549 (1987); and L. E. Fencil, et al.: "Accurate Analysis of Blood Vessel Sizes and Stenotic Lesions Using Stereoscopic DSA System", Invest Radiol 23:33 (1988).) However, neither absolute vessel size nor percent stenosis directly reveals the functional significance of stenosis, i.e., the hemodynamic effect on blood flow.
The relationship between the degree of stenosis and the functional significance of stenotic regions in coronary arteries has been investigated by Gould et al.: "Experimental Validation of Quantitative Coronary Arteriography for Determining Pressure-flow Characteristics of Coronary Stenosis", Circulation 66:930 (1982), who found that classical fluid-dynamics equations were applicable to tapering stenoses in flexible coronary arteries in vivo. Although this implies that the pressure-flow relationship that characterizes the severity of stenosis can be predicted from the degree of stenosis, the determination of the functional significance still requires the measurement of actual pressure gradients across the stenotic region or the measurement of blood flow rates, i.e., the volume of blood flowing through the vessel per unit time. Because measurement of pressure gradients requires the insertion of a pressure probe near the stenotic region (a difficult clinical procedure), methods to determine blood flow rates have been studied by many investigators as described in detail below. It should be noted that blood flow rates can be measured by using an electromagnetic flow probe. However, this method also requires the placement of a sensor near the stenosis, and is considered undesirable in clinical practice due to the invasive aspect of this procedure.
Blood flow rates, can be calculated using the cross-sectional area of the vessel and the velocity of blood, as shown in FIG. 1. The accuracy of the calculated flow rates will depend on the accuracy of the estimation of the cross-sectional area as well as the accuracy of the velocity measurements. Therefore, blood flow rates determined from angiograms are expected to be more accurate than those estimated using magnetic resonance or ultrasound techniques because of the high spatial resolution of angiographic images.
In angiography, images are acquired as a temporal sequence while a bolus of contrast material proceeds through a vessel. The image contrast of an opacified vessel at any particular location usually changes from one image to the next, i.e., the image contrast of the vessel is a function of time. For analysis by the computer, the angiograms are digitized by converting the optical density in each area (pixel) of the image to numerical values (pixel values). The vessel contrast is defined here as the difference between the pixel value at the center of opacified vessel and the pixel value in the adjacent background. The vessel contrast is related to the concentration of the contrast material in the vessel. FIG. 2 illustrates the change of the vessel contrast as a function of time. This curve (or any similar curve in which other quantities related to vessel contrast, such as concentration and film density, is plotted) is often referred to as a time-density curve. Note that in this curve the vessel contrast increases as the contrast bolus arrives and then decreases as the bolus proceeds farther along the vessel.
A number of investigators have attempted to measure blood flow rates from angiograms (see F. K. Schmiel, et al.: "Densitometric Measurements of Coronary Blood Flow. Methodological Improvement", Roentgen Video Techniques for Dynamic Studies of Structure and Function of the Heart and Circulation, P. H. Heintzen and J. H. B. Buersch (eds). Georg Thieme Publishers (Stuttgart: 1978), pg. 49; P. Spiller, et al.: "Measurements of Systolic and Diastolic Flow Rates in the Coronary Artery System by X-ray Densitometry", Circulation 68:337 (1983); G. Forbes, et al.: "Phantom Testing of Peripheral Artery: Absolute Blood Flow Measurement With Digital Arteriography", Invest Radiol 20:186 (1985); D. L. Parker, et al.: "Flow Measurements From 3D Reconstruction of Moving Arterial Beds From Digital Subtraction Angiography", Computers in Cardiology, IEEE Computer Society 817:281 (1986); D. K. Swanson, et al.: "Arterial Blood-flow Waveform Measurement in Intact Animals: New Digital Radiographic Technique", Radiology 161:323 (1986); and L. E. Fencil, et al.: "Measurements of Absolute Flow Rate in Vessels Using a Stereoscopic DSA System", Phys Med Biol 34:659 (1989)). Vessel cross-sectional areas were estimated from the measured vessel size by assuming a circular cross section for the vessel. Vessel sizes in the images were determined either from the full width at half maximum of the vessel profile or from densitometric methods. Magnification factors and lengths of vessel segments were estimated by placement of calibration rods, balls, or grids near the vessel of interest, or by using the biplane imaging technique.
Most of these investigators determined velocity of the bolus by estimating the amount of time (the time of transmit) required for the bolus to traverse the 1 distance between two locations in the vessel. The time of transit is usually estimated from time parameters calculated from the time-density curves which were obtained at specified locations in the vessel. It should be noted that a number of time parameters may be determined from these curves, namely, the time that the bolus arrives (Ta), the time that the vessel contrast reaches one-half its maximum value (Thp), the time that the vessel contrast reaches its maximum or peak value (Tp), and the mean transit time (MTT) of the bolus, which is obtained from the first moment of the time-density curve. For steady-flow conditions, accurate flow rates have been calculated using Tp and MTT. However, for pulsatile-flow conditions, such as in arterial flow, the flow rates calculated using MTT and Tp have been found to vary by as much as one-hundred percent of the average flow rates, and the average error in the calculated flow rates is approximately twenty percent.
FIGS. 3a and 3b show comparisons of flow rates obtained by using MTT ant Tp, respectively (circles), and those measured by an electromagnetic flow meter (lines). The solid line indicates the average flow rates, and the dashed lines indicate the minimum and maximum flow rates as measured by the electromagnetic flow meter. It is apparent that the measured flow rates obtained from the analysis of the time-density curves fluctuate considerably about the line indicating the average flow rate and lie between the minimum and maximum flow rates measured by the electromagnetic flow meter.
These results may be understood by considering a pulsatile flow pattern, as represented in FIG. 4, as measured by the electromagnetic flow meter. During the pulse cycle of approximately one second, the flow rate peaks sharply for the period of approximately one-fourth second and is relatively low for the rest of the cycle. It should be noted that the flow rate obtained by analysis of time-density curves is approximately the average flow rate during the time of transit. Thus, for pulsatile flow conditions, the flow rate obtained from analysis of time-density curves will depend on the portion of the pulse cycle over which the time of transit occurs, and consequently the measured flow rates will fluctuate between the minimum and maximum flow rates.
Another important factor which probably contributes to the observed inaccuracies in measured flow rates is the change in the shape of the time-density curves due to the pulsatile nature of the flow. This was observed (see J. H. Buersch: "Use of Digitized Functional Angiography to Evaluate Arterial Blood Flow", Cardiovasc Intervent Radiol 6:303 (1983)) in data obtained from a pig aorta and also in vessel phantom studies performed by the present inventors. FIG. 5 shows the time-density curves obtained at locations spaced uniformly along the vessel. Although the overall trends appear similar, it is obvious that the shapes of the curves are considerably different. Therefore, the time parameters determined from these curves are expected to be poorly correlated. Thus, the calculated flow rates will be unreliable.
These results indicate that techniques which employ time-density curves cannot provide reliable estimates of flow rates under pulsatile conditions. Thus, these techniques will probably not be useful in the clinical setting.
Rather than analyzing time-density curves, Swanson et al., supra, attempted to determine the distance that a bolus of contrast material moves between two acquisitions by comparing the total radiographic densities in regions of interest (ROIs) in images of arteries. Note that the radiographic density is related to the vessel contrast. Note also that the total radiographic densities in the two ROIs will not be equal in general because contrast material flows into and out of the ROIs as the blood flows through the vessel. When the total radiographic densities are not equal, the position of the ROI in the second image is shifted iteratively until its total radiographic density is equal to that of the ROI in the first image. The distance that the second ROI is shifted is considered to be the distance that the bolus traversed between the two acquisitions. The flow rate of the bolus is then determined using this distance, the frame rate (or time interval between image acquisitions), and the cross-sectional area of the vessel which is estimated from the measured vessel size using a circular cross-section model. The peak and mean flow rates presented in their studies indicate a 20-25% error in the estimation of flow rates. This may be partly due to inaccuracy in the geometrical measurements such as magnification and vessel cross-sectional area. Additional factors could be the implicit assumptions that contrast material uniformly fills the vessel and that the X-ray beam quality remained constant during the acquisitions. In addition, the orientation of the vessel axis relative to the X-ray beam and the position of the vessel in the image are assumed to remain constant. Thus, this technique would not be applicable to curved or moving vessel segments.
Parker et al., supra, determined the velocity of the bolus using the distance that the leading edge of the bolus traversed between frames. Their calculated flow rates were consistently 18% higher than the flow rates determined using an electromagnetic flow meter. This overestimation may be due to diffusion effects at the front edge of the bolus. An additional source of error could be attributed to the effects of laminar flow. In the case of laminar flow, the velocity of the fluid at the center of the vessel is twice the average velocity in the vessel. It should be noted that for angiographic techniques, the flow rate measured is that of the region occupied by the contrast material. The contrast material of the leading edge of the bolus tends to be located in the center of the vessel. Thus, methods which use only the leading edge to measure flow rates will probably always overestimate flow rates.
The digital images used in the phantom study by Fencil et al., Phys. Med. Biol. 34:659 (1989), supra, were obtained with a Digitron 2 DSA system (Siemens Gammasonics, Des Plaines, Ill.). All images were acquired with a matrix size of 512.times.512 and a pixel size of 0.36 mm. The image data from the Digitron 2 were analyzed with a VAX 11/750 computer (Digital Equipment Corporation, Maynard, Mass.) connected to a Gould-DeAnza FD5000 image processor and CRT display. The vessel phantom consisted of non-distensible tygon tubing with a 6.7 mm nominal inner diameter. The phantom was imaged with a 9 cm thick lucite plate which provides scatter. A pulsatile pump (Harvard Apparatus, South Natick, Mass.) was used for supply of 0.9% normal saline solution through the phantom. Instantaneous as well as average flow rates were measured with a 6.7 mm extracorporeal flow probe and a Cliniflow electromagnetic flowmeter equipped with a strip chart recorder (Carolina Medical Electrons, King, N.C.). The pulsatile frequency of the pump was maintained at 1 Hz, and experiments were performed for average flow rates ranging from 200 to 650 cc/min. Up to 58 images were acquired at 15 frames/sec, as an injection of 2 cc of Renographin was delivered with an Angiomat 3000 injector (Liebel-Flarsheim, Cincinnati, Ohio) over 0.25 to 0.5 sec.